Let's review a few key points.
1: Fast Not Slow. Spicer said that President Trump first heard about Flynn's deceptions on January 26th, after Acting Attorney General Sally Yates informed the White House Counsel about it. Spicer says there was a slow erosion of trust which led over almost three weeks to Flynn's ouster on February 13th. This makes no sense at all. Flynn appears to have maintained all his access to the center of the national security process right up until the day he was fired. Mere hours before his ouster top administration officials were still saying he had the full confidence of the President. And the White House had no replacement at the ready when Flynn was fired. These and many other reasons point overwhelmingly to the conclusion that Flynn's firing was a sudden decision, triggered by leaks which confirmed both his deceptions (2/9) and the DOJ warning (2/13).
2: No Mention of the President. Spicer awkwardly asserted a few key claims - that President Trump did not authorize the sanctions conversation with the Russian Ambassador and that he did not know about it until the DOJ warning. These were not categorical denials. But Spicer found his way to denying them. But throughout, Spicer conspicuously did not say that the Flynn misled the President. This is not an accident. It's a key to the story. It simply makes no sense and most likely means the President knew what had happened all along.
3. Trump Knew It Was Okay. Spicer repeatedly stated that President Trump "instinctively" knew that what Flynn had done was okay and that Trump's chief lawyer later confirmed this. (Spicer used the term "instinctively" at least three times.) No one thinks this was okay. Whether it violated any statutes is highly uncertain. It's not okay. If it were, why would Flynn have lied about it repeatedly? This is a highly odd statement which seems to allow for the President to acknowledge later either knowing about or authorizing the conversation.
4: And Trump Was Definitely Right. The consistent theme of Spicer's argument was that there was no legal or substantive problem with what Flynn did. Indeed, the President "instinctively" knew it was okay. The only issue was that Flynn misled the Vice President and others. In other words, there's no "Russia" issue here at all, simply an internal White House issue of the President losing confidence in the honesty of a key staffer. This is demonstrably not true. The need to insist it is strongly suggests that others in the White House, namely the President, is implicated in the Russia issue. Otherwise, it would make political sense and be eminently fair to toss Flynn to the wolves.
5. Desperate Not Serious. Handling a White House briefing in this climate would be a challenge for anyone. But Spicer is palpably not up to the challenge. This was clear in awkward pauses, pained attempts at humor, etc. But he made a number of claims that were clearly pre-planned. The most glaring instance of this was blaming the Department of Justice for not informing the White House soon enough. This isn't just ridiculous. It's not simply a typically Trumpian effort to shift blame, often in nonsensical ways. It shows panic and desperation.
Everything about this story suggests that the White House has many secrets to hide and little of the time to prepare, the competence to execute or the cooperation of the President to hide them effectively.
The story makes no sense. That's because it's not true. They didn't even have enough time to concoct a tight cover story.